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On Maximum Common Subgraph Problems in Series-Parallel Graphs

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Combinatorial Algorithms (IWOCA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8986))

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The complexity of the maximum common connected subgraph problem in partial k-trees is still not fully understood. Polynomial-time solutions are known for degree-bounded outerplanar graphs, a subclass of the partial 2-trees. On the contrary, the problem is known to be NP-hard in vertex-labeled partial 11-trees of bounded degree. We consider series-parallel graphs, i.e., partial 2-trees. We show that the problem remains NP-hard in biconnected series-parallel graphs with all but one vertex of degree bounded by three. A positive complexity result is presented for a related problem of high practical relevance which asks for a maximum common connected subgraph that preserves blocks and bridges of the input graphs. We present a polynomial time algorithm for this problem in series-parallel graphs, which utilizes a combination of BC- and SP-tree data structures to decompose both graphs.

This work was supported by the German Research Foundation (DFG), priority programme “Algorithms for Big Data” (SPP 1736).

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  1. 1.

    We call vertices of SP- and BC-trees nodes and vertices of the input graphs vertices.

  2. 2.

    If an instance of NMwTS does not allow the construction of \(D^{v}_{w}\), all values are multiplied by 3.


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Correspondence to Florian Kurpicz .

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Kriege, N., Kurpicz, F., Mutzel, P. (2015). On Maximum Common Subgraph Problems in Series-Parallel Graphs. In: Jan, K., Miller, M., Froncek, D. (eds) Combinatorial Algorithms. IWOCA 2014. Lecture Notes in Computer Science(), vol 8986. Springer, Cham.

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